Has there ever been helicopter vs. helicopter combat?

This may be a disappointing answer. Helicopters are support platforms, not air to air interception craft like the role a traditional fighter plane fills. While a helicopter may be relatively fast and maneuverable compared to the ground forces they are engaging and supporting, they are not generally capable of flying unsupported and engaging other aircraft. Doing so would be a poor use of resources when there are much more capable machines for that role. Modern military doctrine calls for air dominance before engaging ground forces, to which a helicopter would be supporting; therefore it is unlikely two helicopters would meet and dogfight.

The US Military, for instance, loosely organized their helicopters into three groupings. The three roles are Transportation/Utility, Observation, and Gunships. Notice that none of these roles fills an interceptor role. The one helicopter that carries air-to-air armament in the US Military is the Kiowa Warrior, a light observation craft. In one of it's many configurations it can carry two Stinger air-to-air missiles.

Gunships are almost universally configured for ground combat. They carry machine guns, cannons, and air-to-ground missiles of in an impressive array of configurations. Comanche and Apache gunships, for instance, generally carry mini-guns, cannons, and TOW missiles for engaging ground targets. Any of these could theoretically be utilized to down an enemy helicopter.

It is entirely possible that two opposing forces helicopters have meet on the field of battle and one fired upon the other; however, I have never come upon it happening in from a reputable source. There are reports of Iraqi helicopters shooting down Iranian helicopters with TOW missiles in 1980 during the Iran-Iraq war, but this has not been confirmed that I am aware of.